SOLUTION: Please help Solve this problem: 2^4x = 8

Question 91335: Please help Solve this problem:
2^4x = 8
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To find x take the logarithm of both sides:
.

.
By the rule for exponents in logarithms, the exponent "4x" can be brought out as the multiplier
of the logarithm on the left side. This converts the problem to:
.

.
Now you can use a calculator to find that and
.
Substitute these into the equation and you have:
.

.
On the left side multiply the 4 times 0.301029995 to get 1.204119983. This becomes the
multiplier of x so the equation is reduced to:
.

.
Solve for x by dividing both sides by 1.204119983:
.

.
So x is equal to 0.75 or its fraction equivalent .
.
There is an easier way to do the problem. Notice that you were given:
.

.
Then notice that 8 equals . If you substitute this for 8 the equation becomes:
.

.
For this to be true, the exponent of 2 on the left side must equal the exponent of 2 on
the right side. Therefore, 4x must equal 3, and when you divide both sides by 4 (the multiplier
of x), the equation becomes . That was quicker and easier. You could also
have done it in the second step of our original solution ... the step where we took the
logs of both sides to get:
.

.
At this stage if you replace 8 by the right side changes and the equation becomes:
.

.
Now the rule of exponents in logs applies to both left and right sides and the equation becomes:
.

.
Then divide both sides by and the log terms disappear from both sides so you
are left with:
.

.
and when you divide both sides of this equation by 4 the result again is:
.

.
Hope this helps you to understand the problem a little better.
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